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Let a , b and c be vectors with magnitude 3 , 4 , and 5 respectively and a+b+c=0 then the value of

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Solution:

\ecause a+b+c=0

Squaring both  the sides

left | a+b+c 
ight |=0\ \Rightarrow left | a 
ight |^2+left | b 
ight |^2+left | c 
ight |^2+2(acdot b+bcdot c+ccdot a)=0\ \Rightarrow 9+16+25+2(acdot b+bcdot c+ccdot a)=0\ \Rightarrow 2(acdot b+bcdot c+ccdot a)=-50\ \Rightarrow (acdot b+bcdot c+ccdot a)=-25

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Deependra Verma

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